The 20-3 victory ensures Connacht are still alive in the pool - sitting in third place, two points behind Toulouse and Saracens - with their final match next Saturday against Sarries at Allianz Park.

However, Lam was disappointed with his side's overall performance and their inability to bag a bonus point which could be vital for their qualification hopes.

"I am happy with the win - you don't take wins lightly in European rugby - but I am also pretty disappointed," he said.

"The outcome is great because we got the win, but ultimately we were not clinical enough, and had so many opportunities right across the board that we didn't take."

Although keeping the Italian visitors try-less, it took Connacht more than 20 minutes to register their first points and they secured their second try through Henshaw in the 43rd minute.

"It was frustrating because early on we lost so many opportunities. The quality of our kicking was inaccurate, we kicked recklessly and not in the right place, and gave the ball away at crucial times," added Lam.

"We now have a big week ahead. Our cup form has been good, but that first game against Saracens (in October) still irks - a case of what could have been."

Of Connacht's chances of reaching the last eight, he remarked: "If Toulouse win at home (against Saracens on Sunday ) then it's all up for second place, so realistically we are right there."

Zebre had high hopes of registering their first ever Heineken Cup win, but they left the Sportsground without a single point.

Second row George Biagi said his side had hoped to build momentum after their victory over Benetton Treviso in the PRO12 last weekend, but they came up short.

"It was very disappointing for us today. In the first half we had a few try-scoring opportunities, but we didn't capitalise, and that really cost us the game. Then every time they came into our half, they scored, so it killed us," he said.

"For us it is very important to get a Heineken Cup win - you are on the world stage and everyone relishes these games, so to come here and not really perform is very disappointing.

"Now we have Toulouse (in the final round). It will not come any easier, but we are playing at home and we will do our best to perform."